help-23

[rocky ferry]

idk how to do multiple line texit commands, but isn't this easier?

$\frac{n^{3}-n}{\sqrt{n^{6}+1}} = -\sqrt{\frac{\left(n^{3}-n\right)^{2}}{n^{6}+1}} = -\sqrt{\frac{n^{6}-2n^{4}+n^{2}}{n^{6}+1}}$

[flat frigate]

b0ngl0rd

[rocky ferry]

$-\sqrt{\frac{\frac{n^{6}}{n^{6}}-\frac{2n^{4}}{n^{6}}+\frac{n^{2}}{n^{6}}}{\frac{n^{6}}{n^{6}}+\frac{1}{n^{6}}}} = -\sqrt{\frac{1-\frac{2}{n^{2}}+\frac{1}{n^{4}}}{1+\frac{1}{n^{6}}}} = -\sqrt{\frac{1-0+0}{1+0}} = -\sqrt{\frac{1}{1}}$

[flat frigate]

b0ngl0rd

[rocky ferry]

imagine there's a limit operator all over that

[thin bridge]

same issues
requiring you to consider the definitions of the absval

[rocky ferry]

as n tends to negative infinity, we can pull the negative out from the limit

[thin bridge]

which i'm assuming what the op takes issue with

[rocky ferry]

i don't remember exactly but it could be something to do with the properties of limits that we don't have to worry about it by pulling the negative factor out from the limit?

[wraith prism]

The method is new to me. So it will take a little time for me to understand and assimilate properly. Btw thank you for it

[thin bridge]

well the principle is essentially the same as evaluating infinite limits for rational functions

[wraith prism]

Yes. It's almost the same but i haven't encountered

|n^3|

In limits so I'm learning this new method

It's easy short way

I have to make it this in my habbit

[thin bridge]

you should've encountered $\sqrt{x^2} = |x|$ earlier in math

[flat frigate]

ℝamonov

[wraith prism]

They used negative sign outside because limit is - infinity?

[wraith prism]

Yes

[thin bridge]

for the limit being considered
n^3 - n is negative and from the definition of the abs val
would be -|n^3-n|
which is equal to -sqrt((n^3-n)^2)

[wraith prism]

-|n^3-n|
Why negative sign outside...mod will handle automatically

[thin bridge]

its the defintion of the abs val

e.g -5 = -|-5|

[wraith prism]

Then remove | |

Ohhh wait

[thin bridge]

and from the abs val, you can convert that to the sqrt of a square

same principle as what I mentioned is being applied, just in a different way

[wraith prism]

It's the same yes

[thin bridge]

divide numerator and numerator by the same expression
use the forms most convenient for manipulation

[wraith prism]

So they square root of it. And it will give always postive value of n

And we want it negative value so we added - sign outside

Can we convert -infinity to +infinity in some way

[thin bridge]

you can do a sub like
u = -n

[wraith prism]

Let me try it

Please check it

I'm stuck at the denominator because of minus

Ohh no i made a mistake while power is 6 so it will be positive

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[lusty spear]

Hi everyone , can someone explain to me why we have the terms perfect matching and maximum matching. Are they referring to the exact same thing ?
On the internet it says that in an unweighted graph every perfect matching is a maximum matching. But is that also the case for the other way around ? And also I assume by that definition that in weighted graphs thats another story , right ?

[lusty spear]

oh nvm I shouldve thought a bit more about the definitions of these two

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[static flare]

can you answer check this

[static flare]

i just need to verify part (c) is 19,24

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[heavy coyote]

Hi!
What video do you recommend if I have gaps in trigonometric function studies?

[brave wolf]

https://khanacademy.org/trigonometry

lots of videos, articles, topics and exercises with solutions

[heavy coyote]

Thank you!

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[languid atlas]

I have a question while solving, do we need to consider the domain of the variable t or have we already defined the domain of x and just need to solve the inequality?

[safe radish]

@languid atlas Has your question been resolved?

[pure agate]

No, t was only used as a substitution to simplify the inequality.

[languid atlas]

and does it work in every case?

[pure agate]

Yes, you will get the same result if you don't use the substitution.

[pure agate]

Do you understand how they came up with the invervals?

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[buoyant dragon]

$(x^2+xy+4x+2y+4)y'=y^2$

[flat frigate]

Hack With Techno Boy

[buoyant dragon]

anyone?

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@buoyant dragon Has your question been resolved?

[buoyant dragon]

<@&286206848099549185> ?

[grim plover]

x^2 + 4x + 4 = (x+2)^2

[buoyant dragon]

stuck ;-;

[lean otter]

@buoyant dragon well first of all you need to factor both sides @buoyant dragon

Once you factor the left side

You know that there will be multiple answers

One side -2 will be an answer for sure

Basically -2 will be an answer for the equation

It’s just once you factor the right side you get (x+2) (x+2)= (x+2) (x-2)

If it’s asking for solutions then x= -2,+2

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[static roost]

?

how do i do this

<@&286206848099549185>

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[pseudo scroll]

Substitute sqrt(u) = x

$\frac{x^2}{x + 1}$

[flat frigate]

NEONPerseus

[sour crane]

pythagoras

[lean otter]

slime?

[flat frigate]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[brave wolf]

this should work, seems like bot's broken

[flat frigate]

pvpb0t

pvpb0t

pvpb0t

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[main flower]

Can someone help

[floral osprey]

maybe make a graph?

that is, a network

then cut out the most expensive line if you can get between the 2 nodes by another path

repeatedly

not sure if that's guaranteed to find the minimal cost network but shrug

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[silver nova]

could i get an answer in logarithm form for 2^2ln2-2^-2ln2 instead of just a decimal?

[silver nova]

i put it into my calculator and get a decimal value but maybe i could do something with logs to get my answer in another form?

<@&286206848099549185>

[pure agate]

$2^{2\ln{2}} - 2^{-2\ln{2}}$

That?

[flat frigate]

Kookiemon

[lean otter]

.

[safe radish]

@silver nova Has your question been resolved?

[silver nova]

No, the lns are separate of the powers

[pure agate]

$2^{2}\cdot \ln{2} - 2^{-2}\cdot \ln{2}$

[flat frigate]

Kookiemon

[silver nova]

yes

[pure agate]

You can factor out ln(2) and then expand 2^2 and 2^-2.

[silver nova]

thanks

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[green fable]

help me with this please

[marsh walrus]

dont suppose you have the answer

i'm wondering if its like

Call them colors A and B

[green fable]

yes

[marsh walrus]

you can have AAAAAB, AAAABB, ..., ABBBBB

regardless of the faces

like, which is which, just the quantities

[green fable]

so the arrangements does not matter here?

[marsh walrus]

hmm maybe theres an easier way to think of this

no, they do matter

just trying to figure out how to start enumerating

[buoyant shadow]

it's 8

[green fable]

yes but how?

[marsh walrus]

idk if you do 5 and 1 thats 6 alone right

or are they really not counting that

[green fable]

ig all the cases are similar with respect to that one colour

[buoyant shadow]

one face
two opposites
two adjacent

then those 3 again but flipped colors

then 2 ways to color 3, which you can't flip

[marsh walrus]

right

that should be 10 though

[green fable]

what didnt get that part

[buoyant shadow]

i don't know how to think about it systematically

[drowsy moss]

it's probably up to rotation of the cube

[marsh walrus]

one from one

two from 2

2 from 3

oh wait the 3 case is symmetric like

so you only gain those 2 one time

[buoyant shadow]

that's not 10

yes

[marsh walrus]

gotcha

this is probably incomprehensible to asker

[green fable]

help I didnt get any of that

[green fable]

yes true

[marsh walrus]

so theyre not counting coloring different faces as distinct

like, if you can rotate or mirror the cube to get the same coloring, its the same

lets just consider a blank cube, and were coloring some faces black

[green fable]

basically arrangements doesnt matter ?

[marsh walrus]

clearly if you only color one face, theres only one case

yea

[green fable]

yes

[marsh walrus]

if you color 2 faces, theres only two choices

color the first

your next choice is to color an adjacent side

or the opposite side

seem fair?

[green fable]

yes

[marsh walrus]

okay, so thats another 2 cases

[green fable]

yes

[marsh walrus]

in the 3 case

[green fable]

we have 3 yes

[marsh walrus]

3 total so far

in the case we color 3 faces

color one side

next you can choose to color adjacent or opposite

[green fable]

2 cases here also

[marsh walrus]

say its adjacent, the next side can either be adjacent one side, or both

[green fable]

1 adjacent 1 opp or 2 adjacent

[marsh walrus]

yea

like 3 in a cluster, or 3 in a line

now flip the colors in your mind

consider a black cube, and were coloring faces white

the hard part is seeing that the 3 case is symmetric

if you choose one set up in black, the same thing appears in white

3 in a cluster of black, the other 3 whites will be a in a cluster

same thing with 3 in a line, youll have 3 whites in a line

[green fable]

so wait

[marsh walrus]

so you dont count them twice

[green fable]

basically I got that 1 face coloured part 1 case, 2 face coloured part 2 cases , 3 case coloued part 2 cases?

right

[marsh walrus]

yea

because 3 is symmetric in white and black, you dont count them twice

but the 1 and 2 cases arent

you count them twice

[buoyant shadow]

also you can't leave an unpainted face

they never say that

but if it's 8 then you can't

[marsh walrus]

they do

i think

[green fable]

oh yeah in 3 colours faces we have only 1 case right ?

[buoyant shadow]

oh yeah, they don;t say paint

[marsh walrus]

i gotta get back to studying

can you take over frowny

🙏

[buoyant shadow]

no we have 2 cases

[green fable]

so sorry but I didnt get that part

[buoyant shadow]

i mean it's not 1 way to paint 3

it's 2 ways

[green fable]

no problem dude thnx for helping me out

[green fable]

2 add 1 opp and 2 opp 1 adjacent right?

[buoyant shadow]

you can make 5 cases, to simplify it

[green fable]

5 how ?

[buoyant shadow]

like say colors are red and blue

1 red 2 red 3 red 4 and 5

[green fable]

yes got that

[buoyant shadow]

1 − 1
2 − 2
3− 2
4 − 2
5 − 1

[green fable]

oh ok got it

5 is similar to one coloured thats why there is 1 case right?

thnx a lot for helping me out man

.close

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[weary crane]

Hi, I was wondering if I could get some clarification on whether or not I am doing this problem right for A pls? (B is asking where it is differentiable, sorry for the mistake). I can do B and C from knowing whether or not I did A right, Thanks!

[weary crane]

I'll see if I can put this in latex lol

might take me a while cuz I never used it

<@&286206848099549185>

nvm I figured it out

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[undone grotto]

Determine $\int\int_D e^{x^2+y^2}\sin(y) dxdy$ where D is $ |y| ≤ x ≤ 1$

[flat frigate]

afeAlway

[undone grotto]

I don't know how to find the antiderivative of this kinda function. I can't use susbstitution or integral by parts etc..

And uhh D is btw a triangle when I drew it. Half of it is under the x-axis while the other half is above. But it is not like single variable meaning it doesn't have to be symmetric in this case.

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[undone grotto]

.reopen

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✅

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@undone grotto Has your question been resolved?

[floral osprey]

well e^(x^2+y^2) = e^(x^2 + (-y)^2)
and sin(y) is -sin(-y)
and the triangle is symmetrical for (y) and (-y)

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[daring hornet]

Can someone help me solve number 13?

[rare flax]

!status

[safe radish]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[daring hornet]

1

[lost laurel]

Why does it say “at the point”??? That point isn’t even part of the function

Goofy exercise

[daring hornet]

Yeah, I’m a little lost on what to do

[lost laurel]

Yeah

Normally it would be like at x=-2 not literally a point

[solid parcel]

You need to take the derivative of the function, then evaluate it at that x and y

Implicit differentiation

solve for y' then plug in

[daring hornet]

Okay, let me work that out real quick

Alright, so I got y=(2/3)x + (1.333333) for the equation of the tangent line

I do think that might be wrong

[solid parcel]

Yeah, I retrieved different

What is your y' expression?

[daring hornet]

I got 4cosy -3x^2 = 6xy and got stumped and tried to solve from that

[solid parcel]

where are your y' terms? don't forget the product rule on the 3xy^2

for example - 4y'cos(y) and there should be one more

y' = dy/dx which will be our m

[daring hornet]

Hang on, let me go through my calculations step by step to find the issue

[solid parcel]

Recall your implicit diff rules - every spot you have a y will result in a y' term since y(x).

[daring hornet]

Would it be possible to see how you solved it out so that way I can compare it to mine?

[solid parcel]

d/dx of 4sin(y) = 4cos(x)y'

d/dx of -x^3 = -3x^2

d/dx of 3xy^2 = 3y^2 + 6xyy' (product rule)

d/dx of 12 = 0

I need to run, but you just need to organize that into your equation and youre good to solve for y' and then the equation of the line

[daring hornet]

Okay, thanks for the help

.close

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[wide cloud]

Test tommorow wanna go to sleep quickly can someone help me work this out real quick, i have the answer already I just want to know that i did my work correctly

[solemn vault]

Square both side

[wide cloud]

so 4x+49 = 3 x^2 -25?

[solemn vault]

wait a min

No

[flat frigate]

Random Guy

[solemn vault]

This is what I meant by square both side

Now simplify each side

Yep

[wide cloud]

am i supposed to put it thru the calc

[wide cloud]

ohhh

ok great thank you i'll read this

[solemn vault]

OK

[wide cloud]

i'll rotate it don't worry

have a good night

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[solemn vault]

OK

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[novel magnet]

how is this incorrect

i literally check it on symbolab too

[granite idol]

not sure. can you flag it?

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[keen glacier]

How do I find the gradient vector given this information? I feel like I'm missing pieces

[keen glacier]

My process has gotten that the gradient is going in the direction of -i+j since it is moving NW - but I'm stuck after that

the rubric looks like this

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@keen glacier Has your question been resolved?

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@keen glacier Has your question been resolved?

[keen glacier]

<@&286206848099549185> 💜

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[keen glacier]

.close

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[misty coral]

have you tried drawing it as the house would appear folded up?

[safe radish]

@modern crane Has your question been resolved?

[fading pasture]

have you tried to picture what the 3d house might look like?

can you describe it to me?

indeed!

you don't know the formula for the volume of a cube, given it's height/base/slant length?

@modern crane

it is simply the area of the base times the height

i meant height, i beg ur pardon

are you familiar with the pythagorean theorem?

equals?

observe any one of the four triangles we can see here. can you tell me the values for the base and the hypotenuse?

why would think so?

this is correct

indeed

correct

,calc 81.9404/2

[flat frigate]

Result:

40.9702

[fading pasture]

that appears to be it

can you determine the height now?

,calc sqrt(91.568397^2 - 81.9404*2)

[flat frigate]

Result:

90.669126659242

[fading pasture]

this is the height

if you're unsure abt this, you need to review applying the pythagorean identity

what do u mean?

yes

hmm

you're right, my bad

,calc sqrt(91.567397^2 - (81.9404/2)^2)

[flat frigate]

Result:

81.890359049864

[fading pasture]

there we go

[flat frigate]

Result:

81.891477218998

[fading pasture]

now that you have the height, i believe you can now easily compute the volume of your house. please remember to type .close to close the channel.

surely you know enough math to multiply and add things. i will not be confirming numerical results for you, i'm sorry.

[safe radish]

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[keen sequoia]

why is the answer not a? ln(2) exists so why is it marked as nonexistent

oh wait

is it because ln(0) doesnt exist?

[lean otter]

for the limit to exist, the left and right limits need to be the same

[keen sequoia]

ohhh and because its defined twice at x = 2 it doesnt exist?

[lean otter]

the left and right limits are different here

they are written in red

[keen sequoia]

hm ok

makes sense

what about this one?

im not even sure how to go about this one

all of them follow the derivative formula

[lean otter]

that last one doesn't

[keen sequoia]

tbh the second one doesnt either actually

theres no f(a+x) - f(a)

its f(x) - f(a)

[lean otter]

make a substitution h=x-a

[keen sequoia]

wdym?

[sudden nova]

The second one is still the definition of the derivative, just with a substitution

[keen sequoia]

but its missing f(a-x) in the numerator

[sudden nova]

Look back at the epilson delta form

normally its

[keen sequoia]

idk what that is 💀

[sudden nova]

Wait what

Did u learn differentiation without the definition of limits

[keen sequoia]

like i have no clue what im looking at

[sudden nova]

Uhh

[keen sequoia]

on a diff example

that mentions differentiable functions

we use derivatives

because its finding the slope

[sudden nova]

I think you should understand the limit first

Maybe its the syllabus or something, but understanding the definition of limits, (although maybe unnecessary for some levels) is very important in understanding more of calculus

[keen sequoia]

well yeah, isnt that this?

[sudden nova]

Uhh to understand why two make sense right

Notice right, h is just a variable

Subbing h=x-a for some variable x and constant a is perfectly reasonable

Then you would have as x-a -> 0
(f(a+(x-a)) - f(x) )/ (x-a)

But notice, as x-a ->0 is the same as x->a

(Well unrigorously)

So its just

Limit x-> a of f(x)-f(a) / x-a

[safe radish]

@keen sequoia Has your question been resolved?

[safe radish]

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[lean otter]

i need help with a quadratical equation or function idk what it is

[lean otter]

so the function looks like this; f(x) = a*x²+4x

so there are 2 variables: x,y
A ball is being thrown 20 meters away positive x direction, and i have to find what "a" is, to see how high the ball is being thrown, since it can be thrown in a high angle and strong, or low angle but fast

and i dont know how to solve it how do i get a

how high is the ball at 20m?

@lean otter

on the ground

yup

so whats y at x = 20?

0

plug it in

well

from where the ball is being thrown its also 0

OH

yup

wait

but

im stuck

cuz a can be higher too

show your worj

[lean otter]

hmm?

like

it could be 1/10 but also 1

then it would hit the ground sooner

cuz u can throw the ball higher and still reach the target

yes

but you could throw it in a higher velocity

but you have this type of function given

try it in desmos

it says the height of the ball depends on the range of the target

so

it could be anything

but it will always reach the target

[lean otter]

yes the range is 20m?

yeah

[lean otter]

nop

you have the function given

look at it in desmos itll make more sense

what is desmos?

put in ax² + 4x

[lean otter]

graphing calculator app

on pc?

or phone

on pc use it in web

ohh damn man

well

u see it?

how do i answer the question tho? like can i calculate it?

yes

plug in and solve :)

what does the 4x define`?

doesnt matter

when i put a into 1

the ball reaches 4 on the x

line

so multiply by 5

huh

or divide? get 0.2 and 20

yes

how do u solve it

hmm

without desmos

a/4?

idk

um

write it down

y(x) = ax² +4x / :4
y(x) = a/4x²+x

thats wrong

u gotta do both sides

ohh

but you should first plug in

yeah

wdym by plug in?

that step did nothing

youre solving for nothing right now

the values you got

0 = a*x² + 4x / -a
-a = x²+4x
x²+4x = -a / sqr
x+4x = sqr(-a) /:4
2x = sqr(-a/4) /:2
a = sqr(-x/4):2

im confused

idk if im trying to reverse it

pleaase help

its not 0 all the time

where is it 0?

idk

we always do that i think

instead of y 0

yes

but where is it 0

well y is 0

at the beginning

and end

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[fickle trail]

Classic snowball melting calculus question, is there another way to write the bottom part that I circled with respect to dV/dt? Looking for how fast the volume is decreasing at the moment the radius is 4 inches

I’m not used to this notation with the tall pipe and value at the bottom, just wondering if I can write that differently?

[obtuse jackal]

V function of r, r function of t
As such V o r: t -> V(r(t)) is a function of t
Find (V o r)'(t) when t is such that r(t) = 4

Makes you really appreciate physic notations

Where you can take a derivative wrt to a certain quantity and evaluate it for a given value of another quantity

And write that very simply

Otherwise for the exercise itself, dV/dt = dV/dr dr/dt by the chain rule
dV/dr|r=4 is known
dr/dt|r=4 is given

Gotta go though

[fickle trail]

.close

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[hearty berry]

pardon my stupidity, however, i have studied in linear algebra that whenever i have an equation such as (AX = D) where A is a matrix what we do is that we multiply both sides by the inverse of matrix A to obtain the column vector X

[hearty berry]

that should be correct however in this example, as you can see he did not get the inverse

[little smelt]

you can you this method too

find inverse is hard, at least that's what I'm thinking

[hearty berry]

thats true, the inverse on matlab was alot of decimlas which would really complicate the solution

[hearty berry]

but isnt it the rule?

how can i just ignore that

it doesnt make sense to me

[little smelt]

Nope. Do you know why we find inverse to solve it?

[hearty berry]

to get X i need to multiply the inverse of matrix A with D

[little smelt]

why inverse make sense to you?

[little smelt]

why?

[hearty berry]

because, the equation is (AX=D)

as there is no division in with matrices then what i have to do is multiply both sides by the inverse of A

which would eventually provide me with X = A^-1 D

[little smelt]

that doesn't answer my question

[hearty berry]

is your question still unanswered?

[little smelt]

still vague

[hearty berry]

then what is your approach to solve such equations

[little smelt]

yep think this way

X is vector, that means 1*n

but A^-1D is n*n right?

[hearty berry]

im sorry but what does n stand for

any number?

[little smelt]

sorry I made mistake

I'm confused sorry

you're right

but think this way... do you know the identity matrix?

[hearty berry]

yeah

[little smelt]

let identity matrix as I

[hearty berry]

alright

[little smelt]

We need to change Ax=D into Ix=B, where B is 1 cross n matrix

that's why we mutiply A^-1 on both sides

that is A^-1 A x = A^-1 D

[hearty berry]

yes

[little smelt]

likewise we just changing A into I

[little smelt]

here

[hearty berry]

yes

[little smelt]

but there's more to it

[little smelt]

you can express the matrix equation into 3 linear equations, do you know that?

[hearty berry]

hmm i do not actually

as 3 column vectors?

or row vectors?

or wait as equations...

[little smelt]

just do matrix multiplication

Do matrix multiplication for Ax

you get equations like a_3x+bx_2+cx_3

for each row

[hearty berry]

ok

im trying it

[little smelt]

like this

but reverse the process

[hearty berry]

oh

[little smelt]

It's what we call system of linear equations

[hearty berry]

oh yeah i know that

i thought you meant something else

[little smelt]

okie so you know how to solve that system of linear equations?

[hearty berry]

supposedly, but i need to have constants on both matrix

[granite idol]

constants?

[little smelt]

I don't get it?

[hearty berry]

oh wait

i do not get it myself

[granite idol]

you can solve by row reduction

[hearty berry]

this part

[little smelt]

in your case a=0.5, b= -0.1, c=-0.1

[hearty berry]

yes yes thats easy, i just dont get what equation we would end up with

[little smelt]

Maybe I'm bad at explaining stuffs

[hearty berry]

ok so we would end up with something like this picture

[little smelt]

yep.

[hearty berry]

and i should get the rref of this?

[granite idol]

yes, but write it as an augmented matrix

[hearty berry]

alright

[granite idol]

they show you exactly the setup in your 2nd picture above

[hearty berry]

like this?

[granite idol]

yes

[little smelt]

I think you should that the course of Gilbert Strang's linear algebra. It's in mit website.

That lectures will help you move forward

[hearty berry]

i am knowledgeable about rref and all of this, my problem is one thing, why didnt we get the inverse of A and put the [85;65;0] vector beside it?

[little smelt]

you can put that too if you wish

[hearty berry]

like this example

[granite idol]

sometimes the inverse doesn't exist

[hearty berry]

in this case it does, but its alot of decimals

but to my understanding it should be mathematically inaccurate to just neglect the inverse

[granite idol]

why? if the inverse exists, you get the same solution

[hearty berry]

as i could have also done that in this example

[little smelt]

Find determinant. If determinant is 0, then inverse doesn't exist

[granite idol]

the larger the matrix, the more tedious it is to find the inverse

and for larger matrices, it is more tedious to find the determinant

[hearty berry]

it is equal to 0.079

on matlab ofcourse

[little smelt]

I think even Mathlab itself use that Gauss-jordan elimination method'

[granite idol]

I think Matlab uses the QR decomposition, but yes they don't outright calculate the inverse

[hearty berry]

so why did we use the inverse here and not in the first example?

[little smelt]

so inverse exit. you can find inverse then solve like you always do

[granite idol]

I don't know, ask your teacher?

[hearty berry]

i see

i will look more into it, but thank you so much both of you, sorry i may have tired you

[little smelt]

No problem

[hearty berry]

.close

[safe radish]

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[hearty berry]

.reopen

[safe radish]

✅

[little smelt]

I think you should take that mit or khan academy course

that might help you to clarify it

[hearty berry]

i will look into them too, i remember khan academy being a really great course, thank you!

[little smelt]

Form my knowledge, I learned inverse method later. At 1 st I learned Gauss-jordan elimination method.

If there's nothing close the channel

[hearty berry]

yeah i have already learnt the gauss jordan, currently supposedly have learned the inverse, yet i am struggling abit with economics applications but i am sure i will manage hopefully

.close

[safe radish]

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[lunar drift]

help

[lunar drift]

hey

how do i do this

?

[lean otter]

use the definition of groups/fields etc

[lunar drift]

oh okay

just all 5?

[lean otter]

5?

[lunar drift]

the laws

commutative associative

neutral element

inverse element

and selcusion

[lean otter]

thats for fields, yes

for groups its only associativity, inverse and neutral

[lunar drift]

whats identity

[lean otter]

neutral

[lunar drift]

oh okay

one more question

is inverse element only available if neutral is given?

and neutral is always 0 or 1 right?=

[lean otter]

0 is the neutral element for +

[lunar drift]

and here

[lean otter]

1 is the neutral element for *

(by convention)

[lunar drift]

yes

and the inverse element with a = neutral element right?=

a + inverse = neutral

[lean otter]

yes, $a\cdot a^{-1}=1$

[flat frigate]

Toby

[lean otter]

and $a+ (-a) = 0$

[lunar drift]

okay

[flat frigate]

Toby

[lunar drift]

AND HERE i send you my results can you check wether its right or not?

oh wait

do you understand the task?

[lean otter]

kind of, I just put it through gtranslate

[lunar drift]

i did (1,2) * (2,1) = 2,2 /// and then (2,1) * (-2,1) = (2(-2), 1 = (-4,1)

for task a

[lean otter]

yeah that looks right

[lunar drift]

ok one more question

on b

whats the fourth sqrt of 1/2 ?

how do i can get it

[plucky elk]

can't be simplified

[lunar drift]

i did (1/2)^4

[plucky elk]

that's not correct

$\sqrt[n]{a} = a^{1/n}$

[flat frigate]

riemann

[lunar drift]

oh okay

thanks

SO ITs 1/4^1/4

?

1/2*

[plucky elk]

you should be able to plug it into a calculator

[lunar drift]

i am not allowed to

without calculator

[plucky elk]

i mean to just check your work

not do it on an exam

[lunar drift]

oh okay

can i send you later the results of a matrix i solve

?

[plucky elk]

you can send as much work here as you want

[lunar drift]

okay thanks

[safe radish]

@lunar drift Has your question been resolved?

[safe radish]

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[oak ibex]

using simple terms, (i cannot use math in english for the love of me), find x where sin x - cos x = (sqrt(3) + 1)/2

[oak ibex]

well, ik it's 5pi/6 but i want proof

[pseudo scroll]

$\cos \frac{\pi}{12} = \frac{\sqrt 3 + 1}{2\sqrt 2}$

Do you know this yourself?

[oak ibex]

no

[pseudo scroll]

I see

Well

[split ether]

pi/12 you mean?

[pseudo scroll]

Oh yeah

[flat frigate]

NEONPerseus

[pseudo scroll]

Good catch

Accept this

It exists

¯_(ツ)_/¯

Without this you cannot really proceed

[oak ibex]

oh

[pseudo scroll]

Not to my knowledge atleast

[safe radish]

@oak ibex Has your question been resolved?

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[old arch]

Sorry for other language

But if 5% are 4 people

How do you calculate properly do see if 80 people are in this pie chart?

[granite idol]

if you let "x" be the total number of people, does that give you a clue for how to set it up?

[old arch]

8 = 8/1?

[granite idol]

no, you didn't use "x"

how can you express "5% of the total population equals 4" in an equation?

[old arch]

5% = 4
x??

I’m confused

[plucky elk]

use fractions

5% of x equals 4.

[old arch]

Anyways

a^n * a^n = a*a^n+n???

[old arch]

Still don’t understand

[plucky elk]

"5% of x" means 0.05 * x

do you know how to solve for x now?

[old arch]

yes

But it’s in percentages

So I can’t do 0.05 * 30%

[old arch]

a^n * a^n = a*a^n+n???

[plucky elk]

i can't read this language

[granite idol]

you asked how can you see if 80 people are represented in the pie chart. I hinted, and riemann outright told you, you can solve "0.05x = 4" for x. do you understand?

[old arch]

Basically, a poll was made and each category is different film.

And the 5% section are 4 people

Now you need to find if 80 people took part in the poll.

So 0.05 * 80?

[granite idol]

@old arch this

[plucky elk]

then why are you trying to multiply 0.05 with 30%?

x is the population you're solving for

[safe radish]

@old arch Has your question been resolved?

[old arch]

I’m confused

I don’t know how to do this

.close

[safe radish]

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[flat frigate]

Epik Gamer

[safe radish]

@lean otter Has your question been resolved?

[stoic dune]

It's a bit hard to know where you are with this question. Have any thoughts on it?

Grogg's answer looks incorrect. Can you follow his reasoning?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[leaden scaffold]

How would I solve part b?

[safe radish]

@leaden scaffold Has your question been resolved?

[safe radish]

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[turbid jetty]

how come according to my teacher's soln. $cos^2(2x) = cos(4x)$

[turbid jetty]

is there a rule of algebra that i've missed?

wait no

ive misread the solution i see now

typing it out made me realise sorry

.close

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[lean otter]

can someone confirm this calculation

[floral osprey]

is the top equation z' = z^2 - 4z

ohh that's an i

[lean otter]

z²-2(1+i)z

[floral osprey]

yeah it looks right to me

[lean otter]

ty

.close

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[normal adder]

Hello, with a fair 6 sided dice, I want to calculate how many rolls it would take to get 10 1's AND 10 2's. How do I do this? I know what the answer should be because I wrote a python script to simulate it but I would like to be able to calculate it to abstract it to other problems. Thanks

[stoic dune]

I assume you mean "expected number of rolls". Should take 60 on average. Just because you should expect to roll 10 of every number

[normal adder]

Yes I did mean that. That was my initial thought as well but the results of my simulation disagrees. https://www.online-python.com/BLnOaQr8kU

[safe radish]

@normal adder Has your question been resolved?

[normal adder]

Also, in the case where you want 10 of every value, the average can't be 60 rolls because 60 is the absolute minimum. So it must increase with each added requirement

[stoic dune]

I can't read python lol. Not my language of choice. I should learn it.

20 is the absolute minimum, but I do see what you're saying. Let me think, maybe I can attach some probability theory to this

[normal adder]

Thank you, the TLDR of the script is it says the expected number of rolls is ~70.5 for 10 1s and 10 2s, and then ~86 to get 10 of all rolls

[mortal sandal]

there's not really any closed form formulas for this, not that I'm aware of

you could get an exact answer feasibly if you use dynamic programming to calculate the distribution

or if you used inclusion-exclusion

[normal adder]

OK thank you. I don't expect you to continue thinking about this but if you do feel free to message me about it. I will continue trying to solve it

[mortal sandal]

inclusion-exclusion is feasible for the 1&2 case

hmm

dynamic programming for the all rolls case would be computationally intensive for sure

dynamic program is essentially

let prob[x][y][n] be the probability that we see at least x 1s and at least y 2s after n rolls

find a procedure to compute each value of prob[x][y][n] based on previous values

[normal adder]

OK sounds interesting, thank you for your help, will probably close the channel now

.close

[safe radish]

Channel closed

Closed by @normal adder

Use .reopen if this was a mistake.

[mortal sandal]

np

[safe radish]

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[scenic holly]

Anyone help with solutions please

[scenic holly]

Condition:
If x = t - 2, then x^2 - t^2 = ?

How to solve this?

[jade magnet]

you can replace x with t-2

idk what the goal is though

[scenic holly]

So t = x + 2, right?

[jade magnet]

sure

[lethal summit]

u cant solve that 😂

[scenic holly]

How to solve that?

[jade magnet]

ye whats the end goal

you want x^2-t^2 as an expression of only x?

[scenic holly]

I don't get what I do wrong but I cant get the right answer

[lethal summit]

im saying u cant u need a value

send a pic of the question?

[scenic holly]

Oh, sorry

You misunderstood

I need to simplify

[lethal summit]

i mean we need atleast 1 variable value

[scenic holly]

Not to solve

[lethal summit]

in terms of x or t?

[scenic holly]

t

[lethal summit]

use (a-b)^2 formula in place of x

[jade magnet]

ah

[scenic holly]

It makes sense, I'll try

[scenic holly]

Could I ask?

x^2 - t^2 = (t - 2)^2 - (x + 2)^2

[jade magnet]

dont substitute for both

(t-2)^2-t^2

only do for x=t-2

[scenic holly]

Okay, thanks

But

I want to ask another

t^2 - 4t + 4, and then -x^2 + 4x + 4, or - (x^2 + 4x + 4)?

[lethal summit]

wait why

the eqn is x^2-t^2

sub t-2 in place of x

so ull get (t-2)^2 - x^2

[scenic holly]

Thanks, I solved already

[lethal summit]

now use the (a-b)^2 form

[scenic holly]

But I ask about another

Thank you

I ask about another

Just look

[lethal summit]

another q?

[scenic holly]

If we had

[scenic holly]

No, look

If we had (t - 2)^2 - (x + 2)^2 -> t^2 - 4t + 4, and

[lethal summit]

it wud be the second one

• (x^2 + 4x + 4)

[scenic holly]

When we expand - (x + 2)^2, is it -x^2 +4x + 4, or

• (x^2 + 4x +4)?

[jade magnet]

2nd one

[lethal summit]

• (x^2 + 4x + 4)

[scenic holly]

Thank you men!

That's what I needed

[jade magnet]

also you would just replace x=t-2 again if that was the case

(x+2)^2=(t-2+2)^2=t^2

[scenic holly]

Yeah, I've already solved this task

[jade magnet]

yea nws

[scenic holly]

.close

[safe radish]

Channel closed

Closed by @scenic holly

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[scenic holly]

Help me again

[topaz tree]

[scenic holly]

Condition: from cities A and B, distance between them equals to 340 kms, at the same time bus and taxi went towards with constant velocities: bus - 65 kms / hour; taxi - 80 kms / hour

Question: show can I calculate the distance S between taxi and bus in x hours after the start of the moving?

[safe radish]

@scenic holly Has your question been resolved?

[true horizon]

could you give us a diagram

[buoyant shadow]

bus from a to b, taxi from b to a

[true horizon]

then they should be approaching each other at 65 + 80 = 145 km/hr, meaning that after x hours the distance between them is (total distance) - (distance covered per hour) * (hours)

as to what happens after they pass each other i'll leave that to you

[safe radish]

@scenic holly Has your question been resolved?

[safe radish]

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• Show your work, and if possible, explain where you are stuck.
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[wary mountain]

how would i factor this

[quasi bison]

by guessing one root and knocking it down to a quadratic

[wary mountain]

wym guessing one root

[brave wolf]

do you know rational root theorem?

[wary mountain]

no

[brave wolf]

and depressed cubics?

[wary mountain]

no

[viscid finch]

Do you at least know wht roots are

[wary mountain]

yes

[viscid finch]

Right so the usual way you do this is by hit and trial

[wary mountain]

is there another way

[viscid finch]

For special cases yes

But there's no generalisation

[brave wolf]

I misread it, nvm

[wary mountain]

ok so i just have to guess

[brave wolf]

yeah

[wary mountain]

ok thanks

[brave wolf]

there is general formula. And for depressed cubics its quite simple

[wary mountain]

.close

[safe radish]

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[plucky yarrow]

Okay can someone explain to me

[plucky yarrow]

How does

Y = -2 (-1) + 4
= 2 + 4
= 6

Where is 2 coming from ??? How did that get to 6???

We're doing y = mx + b, how to graph an equation???

[jade magnet]

-2(-1) is -2 * -1 = 2

and 2+4=6

[lean otter]

it multiplied with -ve one

[plucky yarrow]

The what

I'm in grade 11 I have no clue what these terms are

[jade magnet]

negative 2 multiplied negative 1

[plucky yarrow]

Like isn't it -2 (-1) multiply or divide ??

[plucky yarrow]

When I do this on calculator it doesn't give me 2 :(

[lean otter]

learn BODMAS first then i guss

[jade magnet]

,calc -2 * -1

[flat frigate]

Result:

2

[plucky yarrow]

We use bedmas here

[plucky yarrow]

Thank you my calculator keeps givin me a different answer

[lean otter]

whats that 🙂

[jade magnet]

you prob type it in wrong

regardless you shouldnt have to use calc for -2 * -1

[plucky yarrow]

Bedmas
Brackets
Exponents
Division
Multiplication
Addition
Subtraction

[plucky yarrow]

Most likely, half the time I press negative before typing the number it takes the negative symbol away

Okay but now how does

Y = -2 (-5) + 4

= 4 + 4

[lean otter]

here its
BODMAS
Brackets
Of
Division
Multiplication
Addition
Subtraction

[plucky yarrow]

= 8?

[jade magnet]

it doesnt

[lean otter]

use brackets

[plucky yarrow]

Okay so if I put -10 in the spot of -5

Does it become 8?

[jade magnet]

no

[plucky yarrow]

Why do my teacher got 0 on the board what the heeeell

I think he forgot to change the answer

Bc we did like 9 questions help

Whats the actual answer to that

😭

[jade magnet]

i cant read shit

is that a 0

[plucky yarrow]

Apparently yes

[jade magnet]

also a random smudge

[plucky yarrow]

-5

[jade magnet]

just do another question

[lean otter]

14

[plucky yarrow]

Hold up okay so

How do I do the math to graph the next equation

What goes in the place of x?

Y = -2 (?) + 4

Oh I graphed it wrong

Nvm hold on.

[lean otter]

the value which u put to get the answer of y